FJRW-Rings and Mirror Symmetry
FJRW-Rings and Mirror Symmetry
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DOI：
10.1007/s00220-009-0929-7
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发表时间：
2009-03
影响因子：
2.4
通讯作者：
Marc Krawitz;Nathan Priddis;P. Acosta;N. Bergin;Himal Rathnakumara
中科院分区：
文献类型：
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作者：
Marc Krawitz;Nathan Priddis;P. Acosta;N. Bergin;Himal Rathnakumara
Landau-Ginzburg镜像对称猜想指出，对于一个可逆的准齐次奇点W及其最大对角对称群G，存在一个对偶奇点W，使得W/G的A模型与W T的B模型同构。Landau-Ginzburg A-模型是由Fan，Jarvis和Ruan构造的Frobenius代数$$\fancySCRIPT{H}_{W，G}}$$，而B-模型是WT的奥比诺德-米尔纳环。我们用最大对角对称群证明了Arnol‘d关于单峰和双峰拟齐次奇点列表的Landau-Ginzburg镜像对称猜想，并讨论了便于计算FJRW-环的八个公理。
The Landau-Ginzburg Mirror Symmetry Conjecture states that for an invertible quasi-homogeneous singularityWand its maximal groupGof diagonal symmetries, there is a dual singularityWTsuch that the orbifold A-model ofW/Gis isomorphic to the B-model ofWT. The Landau-Ginzburg A-model is the Frobenius algebra $${\fancyscript{H}_{W,G}}$$ constructed by Fan, Jarvis, and Ruan, and the B-model is the orbifold Milnor ring ofWT. We verify the Landau-Ginzburg Mirror Symmetry Conjecture for Arnol’d’s list of unimodal and bimodal quasi-homogeneous singularities withGthe maximal diagonal symmetry group, and include a discussion of eight axioms which facilitate the computation of FJRW-rings.